NDA Math Mock Test 02 – Mathematics

Question: Consider the vectors \(\vec{a} = \hat{i} – 2\hat{j} + \hat{k}\) and \(b = 4\hat{i} – 4\hat{j} + 7\hat{k}\). What

Question: The two lines x = ay + b, z = cy + d; and x = a’y + b’,

Question: If two vectors \(\vec{a}\) and \(\vec{b}\) are such that \(|\vec{a}| = 2\), \(|\vec{b}| = 3\) and \(\vec{a} \cdot \vec{b}

Question: Find the direction cosines of the vector joining the points A(1, 2, −3) and B(−1, −2, 1), directed from

Question: The position vectors of the points A, B, C are \(2\hat{i} + \hat{j} – \hat{k}\), \(3\hat{i} – 2\hat{j} +

Question: The angle between the vectors \(\hat{i} – \hat{j}\) and \(\hat{j} – \hat{k}\) is सदिशों \(\hat{i} – \hat{j}\) और \(\hat{j}

Question: If \(\vec{a}\) and \(\vec{b}\) are vectors such that \(|\vec{a}| = \sqrt{3}\), \(|\vec{b}| = 2\) and \(\vec{a} \cdot \vec{b} =

Question: The scalar product of the vector \(\hat{i} + \hat{j} + \hat{k}\) with a unit vector along the sum of

Question: The points A(5, −1, 1), B(7, −4, 7), C(1, −6, 10) and D(−1, −3, 4) are the vertices of

Question: The point (−2, −3, −4) lies in the बिंदु (−2, −3, −4) किस अष्टांश (octant) में स्थित है? Options: